Rossby vortices, spiral structures, solitons : astrophysics and plasma physics in shallow water experiments

1. Introduction.- 2. The Natural Phenomena Simulated in Rotating Shallow Water Experiments.- 2.1 Length, Rotation Velocity, and Lifetime of the Structures.- 2.2 Large-Scale, Long-Lived Rossby Vortices in the Atmospheres of Giant Planets. The Cyclone-Anticyclone Asymmetry.- 2.3 Rossby Vortices in the Oceans.- 2.3.1 Open Sea Vortices.- 2.3.2 Rings of the Gulf Stream and the Kuroshio Current.- 2.3.3 Internal Thermoclinic Vortices (Lenses).- 2.4 Spiral Structures in Galaxies.- 3. Common Features of the Simulated Natural Phenomena.- 3.1 Quasi-Two-Dimensionality.- 3.2 Structure Generation by Flows with Horizontal Velocity Shear.- 3.3 Horizontal Dimensions Exceeding the Characteristic Rossby Radius.- 4. Physical Prerequisites of the Laboratory Simulation of Large-Scale Rossby Vortices and Galactic Spiral Structures.- 4.1 The Analogy Between Two-Dimensional Gas Dynamics and the Dynamics of Shallow Water.- 4.1.1 Theory.- 4.1.2 Experiment.- 4.2 Principal Similarity Parameters in Nature and Experiment.- 5. Physical Basis for the Experimental Investigation of Rossby Solitons and Laboratory Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 5.1 Two-Dimensional Motion of Charged Particles in Magnetized Plasma and Particles in Rotating Shallow Water.- 5.2 General Nonlinear Equation for Drift Motion.- 5.3 Linear Rossby Waves and Plasma Drift Waves.- 5.4 Linear Packet of Rossby Waves and the Time of its Dispersion Decay. Definition of a Soliton.- 5.5 Nonlinear Rossby Waves: Vortices and Solitons.- 5.6 Viscous Damping of Rossby Vortices.- 6. Experimental Configurations.- 6.1 Geometry and Rotation Regime of the Vessels for the Observation of Rossby Solitons.- 6.2 Techniques for Local Generation of Rossby Vortices.- 6.3 Devices for Generating Rossby Vortices by Counterflows.- 6.4 Devices for the Simulation of Galactic Spiral Structures.- 6.5 Diagnostic Techniques.- 7. Laboratory Simulation of Rossby Vortices and Solitons in Planetary Atmospheres and Oceans.- 7.1 Generation of Rossby Vortex Chains by Zonal Counterflows in Rotating Shallow Water. The Cyclone-Anticyclone Asymmetry.- 7.2 Self-Organizing Solitary Anticyclonic Rossby Vortex in Zonal Flows as a Model of Jovian Great Red Spot.- 7.3 Regularity in the Generation of Chains with Different Numbers of Vortices and the Problems of Uniqueness and Stationarity of the JGRS.- 7.4 Two- and Three-Dimensional Models of the JGRS.- 7.5 Alternative JGRS Laboratory Models.- 7.6 Stationary Rossby Vortices in Flows and the Blocking Phenomenon.- 8. Laboratory Simulation of Galactic Spiral Structures.- 8.1 Generation of Spiral Structures in Differentially Rotating Shallow Water.- 8.2 Spiral-Vortex Structures.- 8.3 The Common Mechanism Generating Solitary Rossby Vortices in Planetary Atmospheres and Spirals in Galaxies.- 8.4 Asymmetrical and Outbranching Spirals.- 8.5 The Influence of Viscosity and Friction.- 8.6 Laboratory Simulation and Astronomical Observations. Predictions for Astronomers.- 9. Rossby Vortices and Solitons in Free Motion.- 9.1 A Short History of the Experiments.- 9.2 Rossby Solitons in the Laboratory and Their Properties.- 9.3 Collisions of Rossby Vortices.- 9.4 Cyclone-Anticyclone Asymmetry.- 9.5 Quasi-Two-Dimensionality of Rossby Vortices. The Non-Principal Role of Viscosity.- 9.6 Vortex-Wave Dualism.- 9.7 Comparison between Experiment and Theory.- 10. Solitonic Model of Natural Vortices.- 10.1 Solitonic Model of the JGRS and Other Large-Scale, Long-Lived Vortices in Planetary Atmospheres.- 10.2 An Alternative Model of the JGRS: Numerical Calculation.- 10.3 Solitonic Vortices in the Oceans.- 11. Dipolar Rossby Vortices.- 11.1 Preliminary Experiments.- 11.2 Dipolar Vortex Decay for Moderate Liquid Depths.- 11.3 Solitonic Properties of Dipolar Vortices for Large Liquid Depths.- 12. Shallow-Water Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 12.1 Prediction of Drift Soliton Properties Based on Shallow-Water Simulation. Drawbacks of the "Purely Wave" Concept.- 12.2 Vortical Mechanism for the Enhanced Diffusion of Plasma Across a Strong Magnetic Field.- 13. Conclusion.- S. Supplements.- References.